Calculating Thermal Expansion in a Steel Cable

[has1993]

Homework Statement

As shown in attachment a steel cable is stretched between two poles. In 20°C temperature the cable remains horizontal (the length of the cable 10m). At a higher temperature θ°C the cable bends like in attachment. The lamp hanging from the mid-point could be thought as weightless. The linear expansion coefficient for steel is 12 * 10^-6. What is the value of θ?

Homework Equations

l' = l [1 + αθ] ------- 1

The Attempt at a Solution

I first used pythagorian to find the expanded length so,

L^2 = 25 + 64 * 10^-4

that gives L = 5.0064
so the total expanded length 2L = 10.0128

And applying it to the (1) equation
I get a value for θ = 126 °C ! obviously absurd.

So anyone got a hint on what I'm doing wrong?

 

[haruspex]

Pls post the steps between calculating the expanded length and getting theta.

 

[ehild]

L^2 = 25 + 64 * 10^-4

that gives L = 5.00064
so the total expanded length 2L = 10.00128

And applying it to the (1) equation
I get a value for θ = 126 °C ! obviously absurd.

So anyone got a hint on what I'm doing wrong?

You miss some zeroes. I think it is just typing error. I got the same result a you.
Edit: We both forgot to divide the change of length by the original length. ehild

 

[haruspex]

Strange - I get 30.7C.
Fractional expansion = 0.000128 = 1.28E-4. Dividing by 12E-6 gives a bit over 10.

 

[ehild]

Strange - I get 30.7C.
Fractional expansion = 0.000128 = 1.28E-4. Dividing by 12E-6 gives a bit over 10.

You are right, I forgot to divide by Lo.

ehild

 

[has1993]

Thks guys. It really helped. I think I've made some miscalculations. But now i get it. :D